Ask question

Ask question

All categories

Nutka1998 [239]

2 years ago

9

The total amount paid on a 35 year loan was $98,000. If the interest rate was 4.1% and compounded monthly, what was the principa

l? Round your answer to the nearest cent.

2 answers:

IRINA_888 [86]2 years ago

7 0

Answer:

$23,392

Step-by-step explanation:

Use the compound interest formula and substitute the values given: $98,000=P(1+.041/12) $^{12(35)}$

Simplify using order of operations:

$98,000=P(1.003416667) $^{420}$

P=$98,000(1.003416667) $^{420}$

P≈$23,392

Levart [38]2 years ago

5 0

Answer:

The principal amount was $23,393.45

Step-by-step explanation:

The total amount paid on a 35 year loan was $98,000 at the rate of interest 4.1%

We will calculate Principal amount by this formula

$A=P(1+\frac{r}{n})^{nt}$

Where A = amount (98,000)

P = Principal amount (P)

r = rate of interest 4.1% (0.041)

n = number of compounding interest monthly (12)

t = time (35 years)

$98,000=P(1+\frac{0.041}{12})^{(12)(35)}$

$98,000=P(1+0.003416)^{(420)}$

$98,000=P(1.003416)^{(420)}$

98,000 = P(4.189386)

= 4.189386P = 98,000

P = $\frac{98000}{4.189386}$

P = 23,392.4494 ≈ $23,392.45

The principal amount was $23,393.45

You might be interested in

A sequence is defined recursively by the formula f(n+1)=-2f(n). The first term of the sequence is -1.5. What is the next term in

levacccp [35]

Given f(n+1) =-2f(n)
here f(n) =f(1) = -1.5
f(n+1) =f(2) = -2 * -1.5 = 3

9 0

2 years ago

Read 2 more answers

The graph of f(x) = |x| is transformed to g(x) = [X + 11-7. On which interval is the function decreasing?

puteri [66]

Answer:

The interval of the decreasing function is (-∞ , -1) ⇒ g(x)

The interval of the decreasing function is (-∞ , 0) ⇒ f(x)

Step-by-step explanation:

* Lets explain how to solve it

- Decreasing function means a function with a graph that moves

downward as it is followed from left to right.

- For example, any line with a negative slope is decreasing function

- Lets look to the attached graph to understand the meaning of the

decreasing function

∵ f(x) = IxI ⇒ green graph

∵ g(x) = Ix + 1I - 7 ⇒ purple graph

- From the graph f(x) translated 1 unit to the left and 7 units down to

form g(x)

- The domains of f(x) and g(x) are all real numbers {x : x ∈ R}

- The range of f(x) is {y : y ≥ 0}

- The range of g(x) is {y : y ≥ -7}

# For f(x)

- The slope of the green line from (-∞ , 0) is negative

- The slope of the green line from (0 , ∞) is positive

# For g(x)

- The slope of the purple line from (-∞ , -1) is negative

- The slope of the purple line from (-1 , ∞) is positive

∵ The line with negative slope represent decreasing function

∴ The interval of the decreasing function is (-∞ , -1) ⇒ g(x)

∴ The interval of the decreasing function is (-∞ , 0) ⇒ f(x)

7 0

1 year ago

Which inequality represent all values of x for which the quotient below is defined??

Liono4ka [1.6K]

Answer:

the answer is b. because x is either grater or equal.

6 0

2 years ago

Read 2 more answers

A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0

1 year ago

Shamir is trying to decide between two cities to travel to

Soloha48 [4]

Answer:

my life sucks so its 3475

Step-by-step explanation:

7 0

2 years ago